Sustainable Development concept (SD) aims to better life for future generations. However, the COVID-19 pandemic has caused tremendous effects on people’s life in several areas. Therefore, the study aimed to investigate the impact of COVID-19 on the selected part of SD indicators in the OECD countries using Self-Organizing Map (SOM). SOM is a kind of artificial neural network (ANN) method, which is an effective clustering method to find hinder non-linear relationships between indicators. The data contained 38 OECD member countries for 11 variables for each country, covering three years (2019-2021). Firstly, descriptive statistics and Spearman rank correlation analysis were used for bivariate analysis. The coefficient of variation was also used to measure the convergence of indicators. Then, it was a two-stage clustering method using SOM and hierarchical clustering methods—the optimal cluster found according to the Silhouette Index and Davies–Bouldin Index, and as three. The convergence of gross domestic product increased gradually to 40.33% in 2019, 42.01% in 2020, and 43.69% in 2021, meaning increasing relative variability of OECD countries. While the mean of the life span was decreased, the share of health expenditure, health expenditure per capita, out-of-pocket health expenditure, and government health expenditure were increased in the study period. According to clustering analysis, the countries had similar characteristics within three years, except Colombia. Also, the USA distinguished very different characteristics from other OECD countries. Although the mean of study indicators varies due to the effect of the pandemic, the change within each OECD country showed mostly similar characteristics within three years.